tokenomics and platform finance -...
TRANSCRIPT
Tokenomics and Platform Finance∗
Lin William Cong† Ye Li§ Neng Wang‡
First draft: December 4, 2018; this draft: August 26, 2019.
Abstract
We develop a dynamic model of platform economy where tokens derive value by
facilitating transactions among users and the platform conducts optimal token-supply
policy to finance investment in platform quality and to compensate platform owners.
Even though token price is endogenously determined in a liquid market, the platform’s
financial constraint generates an endogenous token issuance cost that causes under-
investment and conflicts of interest between insiders (owners) and outsiders (users).
The franchise value (seigniorage) incentivizes the owners to buy back and burn tokens
out of circulation, reducing token price volatility. Blockchain technology is crucial for
token-based platforms because it enables platform owners to commit to predetermined
rules of token supply that can significantly improve efficiency by addressing platform
owners’ time inconsistency and mitigating under-investment.
Keywords: Blockchain, Cryptocurrency, Dynamic Corporate Financing, Financial
Constraint, Gig Economy, Token and Coin Offerings, Optimal Token Supply.
∗We thank Maureen O’Hara, Sebastian Gryglewicz (discussant), Dmitry Orlov (discussant), Jean-CharlesRochet, Fahad Saleh (discussant), and David Skeie (discussant) for helpful feedback. We also thank confer-ence and seminar participants at ABFER/CEPR/CUHK Financial Economics Symposium, Central BankResearch Association 2019 Meeting, CEPR ESSFM Gerzensee, Chicago Financial Institutions Conference,City University of Hong Kong, Econometric Society North America Annual Meeting (Atlanta), ErasmusLiquidity Conference, Luohan Academy First Digital Economy Conference, Maastricht University, MidwestFinance Association (Chicago), Tokenomics International Conference on Blockchain Economics, 4th RomeJunior Finance Conference, Security and Protocols, and USI Lugano for helpful comments and discussions.Will is grateful for the financial support from the Ewing Marion Kauffman Foundation. Ye is gratefulfor the financial support from Studienzentrum Gerzensee. The contents of this publication are solely theresponsibility of the authors. The paper subsumes a previous draft titled “Token-based Corporate Finance.”†Cornell University Johnson Graduate School of Management. E-mail: [email protected]§The Ohio State University Fisher College of Business. E-mail: [email protected]‡Columbia Business School and NBER. E-mail: [email protected]
1 Introduction
Over the past decades, digital platforms and online networks have received mounting in-
terest, and are reshaping the organization of economic activities. Many successful platforms
rely heavily on payment innovations (e.g., Alibaba and eBay) because the lack of trust among
dispersed agents presents a major obstacle for economic exchanges. The blockchain technol-
ogy rises to this challenge by allowing the creation of crypto-tokens as the local means of
payment among platform users and providing consensus on transaction records to overcome
problems of digital currency such as double-spending. Proven payment innovations (e.g., es-
crow account) can also be conveniently implemented via smart contracting, facilitating not
only the economic exchanges among platform users but also the recruitment of on-demand
labor and resources by the platform for its ongoing development.
Despite practitioners’ enthusiasm, the economic trade-offs in managing platform tokens
remain unclear. How are token prices determined by user activities (trading and usage) and
platforms’ token supply? How much should platforms invest in its productivity and pay
contributors with tokens? How do platform owners profit from token-supply management?
What do blockchains and smart contracting bring to both centralized and decentralized
platforms? To take a first step in answering these questions, we propose a tractable dynamic
framework for designing tokens and managing platform development.
Specifically, we build a continuous-time model of platform economy that captures the
monetary, asset-pricing, and corporate-finance aspects of tokens. Because the platform is a
unique marketplace for certain transactions, platform users demand tokens for a convenience
yield. Platform owners manage the token supply. Token supply increases when the platform
owners issue tokens to reward themselves or to pay decentralized contributors to enhance
platform productivity. Contributors sell tokens to users (the ultimate token holders) for
consumption goods. Token supply decreases when the owners raise external financing (con-
sumption goods) to buy back and burn tokens out of circulation. Token buyback incurs a
financing cost, so the platform operates in a realistic environment of investment, financing,
and payout akin to Bolton, Chen, and Wang (2011). Our model differs because financial
slack comes from token-supply management instead of cash management, and the token price
is endogenously determined as the users’ demand meets the owners’ supply. Our model also
differs from a majority of monetary-policy models because tokens as means of payment are
issued to finance investment as in Bolton and Huang (2017) rather than stimulates nominal
aggregate demand or alleviates liquidity shortage.
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To capture users’ network effects, a distinguishing feature of platform businesses, we allow
tokens’ convenience yield to depend on the aggregate number of users (“user base”). The user
base evolves endogenously because users’ participation depends positively on the platform’s
productivity (through the convenience yield) and their expectation of token price change.
An intertemporal complementarity in user base arises — when potential users expect the
platform to improve and more users to join in future, they expect token price to appreciate
and thus participate more now.
Tokens not only allow users to transact with each other, but also allow the platform to
access a pool of dispersed contributors for their effort and resources that can improve platform
productivity. Because the contributors sell tokens to users who are the natural buyers of
tokens for their convenience yield, the amount of resources the platform can raise through
token payment depends on the users’ valuation of tokens. Intertemporal complementarity in
user base makes it crucial for the platform owners to invest in productivity growth.
The owners’ value is the present value of all tokens paid to themselves net of the costs of
token buy-back. In a Markov equilibrium, it is a function of the current platform productivity
and token supply, which are the two state variables. The marginal value of productivity is
positive, capturing the equilibrium dynamics of users’ adoption and valuation of tokens. The
marginal value of increasing token supply is negative because of the downward pressure on
equilibrium token price. Therefore, when deciding on token issuance, the platform owners
face a trade-off akin to that of durable-good producers. The distinction is that our model
features endogenous investment and, as will be emphasized shortly, financial frictions. The
resistance against excessive supply also applies to the platform’s payout policy, i.e., tokens
paid to the owners themselves, and encourages the owners to buy back tokens and burn them
out of circulation in order to protect their continuation or franchise value.1 In equilibrium,
the ratio of token supply to platform productivity emerges as a key signal that drives platform
investment. The payout and buyback impose two reflecting boundaries on the ratio.
A key inefficiency in our model is that when buying back tokens, the platform owners
have to raise costly external funds. While token buyback occurs occasionally, the associated
financing cost propagates into a dynamic token issuance cost because the platform owners
1Burning cryptocurrencies or tokens means sending them to a public “eater address” from which theycan never be used again because the private key of such an address is unobtainable. Practitioners often burntokens to boost token value and reward token holders (e.g., Binance and Ripple). Some also use Proof-of-Burn as an environmentally friendly alternative to Proof-of-Work to generate consensus (e.g., Counterparty(XCP) blockchain), or destroy unsold tokens or coins after an ICO or token sale to maintain fair play (e.g.,Neblio’s burning of unsold NEBL tokens).
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foresee costly buyback in future. Specifically, the owners’ cost of issuing one more token,
i.e., the decline of their franchise value, is larger than the users’ valuation of tokens. This
wedge causes the platform to under-invest in productivity enhancement, which in turn leads
to lower user welfare. This divergence of owners’ and users’ interests is quite intuitive. From
the platform owners’ perspective, more tokens in circulation now implies a higher likelihood
of token buyback and incidence of financing cost in the future. The benefit of token issuance
for productivity enhancement is shared with users via a higher convenience yield of tokens,
while the benefit of token buyback is shared with users via token price appreciation. Yet
platform owners fully bear the financing cost.
After characterizing the platform owners’ optimal token-management strategy (i.e., in-
vestment, payout, and buyback), we formally analyze the value added of blockchain technol-
ogy in our setting. A defining feature of blockchain is the irreversible record-keeping, which
enables the encoding of predetermined and invariable token-supply rules. Such commit-
ment is valuable in the presence of conflicts of interest between users and platform owners.
Specifically, motivated by Ethereum (one of the most popular blockchain applications by the
token market capitalization), we consider a constant growth of token supply that finances
decentralized contributions for productivity enhancement.
We find that commitment mitigate the under-investment problem by severing the state-
by-state linkage between platform investment and the dynamic token issuance cost. While
the increased amount of token issuance for productivity enhancement results in more frequent
costly token buyback, the owners’ value is higher than the no-commitment case due to the
increase of token price driven by a fast trajectory of productivity and user-base growth. Our
analysis of the commitment value from blockchain technology highlights the key differences
between blockchain-based platforms and traditional centralized platforms, and thus partially
explain why tokens become popular after the blockchain technology becomes available.
Our model also provides insights on the design of stablecoin. Different from the existing
approaches based on open market operation or collateralization, the platform owners in our
setting support their franchise value by occasionally burning tokens out of circulation. When
the token supply is high relative to the platform productivity — precisely at the moment that
token price is low but the marginal value of reducing token supply is high — the platform
owners burn tokens. Consequently, token supply dynamics moderate price fluctuations. In
our model solution, even though we allow the platform quality to randomly evolve with an
annual volatility of 200%, the volatility of token price change is less than 10%. Committing
to token-supply rules via blockchain further stabilizes token price.
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Overall, by characterizing the token-based interactions among users and platform owners,
our model reveals key trade-offs in the dynamic allocation of tokens. It also provides a
guiding framework for practitioners: The various token offering schemes observed in real life
can be viewed as special (sub-optimal) cases under (perhaps unnecessary) restrictions. Many
existing platform businesses can also benefit from tokenization as discussed in this paper.2
We recognize the control right of platform owners and their discretion over token manage-
ment and platform development. Our focus on platform owners is natural because without
token distributions to themselves, the founders would either not launch the platform in the
first place or design it in a way that allows future profits in other forms (e.g., stealing tokens
from the users or financial contributions from the workers). In other words, token dividends
compensate the founders’ essential human capital.3 Therefore, platform design, and in par-
ticular, the token supply, should be incentive-compatible and time-consistent, allowing the
owners to dynamically extract rents in the form of token dividends. Such design is the only
credible design to users (and regulators) who form expectation of token usage and valuation.
Literature. Our paper contributes to the literature on digital platforms. Classical studies
(e.g., Rochet and Tirole, 2003) do not consider the use of tokens as platform-specific means of
payment. We build on Cong, Li, and Wang (2018) that studies dynamic token valuation and
inter-temporal linkages in user adoption. Our model differs by allowing endogenous platform
productivity and endogenous token supply so that we can analyze the dynamic investment,
financing, and payout policies of platforms and how blockchain technology adds value by
enabling commitment. We share the view on platform token with Brunnermeier, James, and
Landau (2019) – a platform is a currency area where a unique set of economic activities
take place and its tokens derive value by facilitating the related transactions. Beyond this,
we emphasize that a platform can invest in its quality, for example, payment efficiency
(Duffie, 2019), and thereby, raise token value. Our paper is the first to formally analyze how
platforms manage their investment and payout through token supply, and provide insights
into the incentives and strategies of platform businesses.
2The video game industry presents a case in which dispersed agents such as production companies,development companies, console makers, mobile phone makers, writers, composers, and importantly, gamers,all contribute to the evolving community. The traditional use of royalties for compensating such decentralizedcontribution is difficult to manage and subject to various agency issues. Microsoft and Ernst & Young (EY)recently designed a blockchain to address the problems and provide transparency (Roberts, 2018).
3The strategies of a platform, or in general a company, lies in the entrepreneurs’ distinctive point ofview on how to create and capture value – it is cannot entirely be outsourced to decentralized contributors(Felin and Zenger, 2018). While ideology might drive some innovation, economists should all recognize thatinnovations on digital platforms is ultimately driven by entrepreneurs’ incentives and strategies.
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The inter-temporal trade-off that platform owners face in deciding the token supply
resembles that of durable goods producers: A platform owner is concerned that an increase
of circulating token depresses the current and future token price, and thus, erode the franchise
value. Unlike in the durable goods monopolist literature (Coase, 1972; Bulow, 1982; Stokey,
1981), our model features endogenous investment in platform productivity, which maps to
endogenous product quality of durable goods, and financial constraints.
We connect platform economics to asset pricing by demonstrating that the token price is
the present value of platform-specific convenience yield. Our treatment of convenience yield
is related to Krishnamurthy and Vissing-Jorgensen (2012) and earlier studies.4 Our contribu-
tion is to incorporate user network effects in convenience yield and study their implications
on user adoption, platform investment, and platform token-supply policies. Relating to
Brunnermeier and Sannikov (2014), we emphasize agent heterogeneity and its asset-pricing
implications. Instead of balance-sheet crises, we model the endogenous formation of user
base given the users’ heterogeneity in deriving convenience yield from tokens.
We also connect the literature on platform economics to dynamic corporate finance, es-
pecially that emphasizing the role of financial slack (e.g., Bolton, Chen, and Wang, 2011).
Instead of cash management for investment and payout, we analyze platforms’ token-supply
strategies when platform investment induces user network effects and, very importantly,
the token price varies endogenously as users respond to token-supply variation.5 From a
methodological perspective, our paper is most related to Li (2017) who studies banks’ dy-
namic issuance of inside money as the price of money fluctuates endogenously in response
to the variation in banks’ supply and producer’s demand. The distinction is that tokens are
outside money (not liabilities of the issuing platform).
Our paper clearly adds to emerging studies on blockchains and cryptocurrencies. We
take the blockchain functionality as given and add to studies examining the dual role of
tokens both among the users and among the miners (e.g., Sockin and Xiong, 2018; Pagnotta,
2018). Relative to other dynamic token valuation models with exogenous token supplies
(Cong, Li, and Wang, 2018; Fanti, Kogan, and Viswanath, 2019), we endogenize the token
supply. We are thus the first to study platforms’ optimal monetary, investment, and payout
policies with both endogenous token pricing and user adoption.6 Importantly, we highlight
4Baumol (1952) and Tobin (1956) emphasize the transactional convenience of money holdings.5The platform owner essentially maximizes the present value of all future seigniorage, our model shares
this basic insight of Cagan (1956).6Related are discussions on the design of cryptocurrencies and tokens as private money (e.g., Chiu and
Wong, 2015; Chiu and Koeppl, 2017). Almost all prior studies focus on Bitcoin or Proof-of-work protocols
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the commitment value of blockchains and smart contracting.7
Furthermore, our paper adds to the discussion on token price volatility and stablecoins.
On the demand side, high token price volatility (e.g., Liu and Tsyvinski, 2018) could be
an inherent feature of platform tokens due to technology uncertainty and endogenous user
adoption (Cong, Li, and Wang, 2018). Saleh (2018) emphasizes that cryptocurrency supply
under proof-of-burn (PoB) protocols can reduce price volatility. We endogenize both the
demand for platform tokens (as opposed to general payment private/decentralized money)
driven by users’ transaction needs and dynamic adoption, and the supply of tokens for
entrepreneurs to extract rent and incentivize decentralized contribution. In particular, we
show that the entrepreneurs’ optimal dynamic token allocation stabilizes token price.
Finally, our paper is broadly related to the literature on crowdsourcing and the gig econ-
omy. While recordkeeping or consensus provision in the form of cryptocurrency mining are
typical forms of decentralized on-demand contributions, resources raised through initial coin
offerings (ICOs) is another salient type. Existing studies on ICOs and crowdfunding focus
on one-time issuance of tokens before the platform launches (e.g., Garratt and Wallace, 2018;
Chod and Lyandres, 2018; Canidio, 2018), yet platforms increase token supply on an on-going
basis (e.g., Bitcoin and Kin). They also center on entrepreneurs’ hidden effort or asymmetric
information, whereas we emphasize decentralized contributors’ effort that is highly relevant
for digital platforms and the gig economy.8
2 Institutional Background
To understand tokenomics and its role in platform finance, some institutional background
is necessary. In this section we discuss how in practice platforms, blockchains, and the use
of tokens are all connected. We also use the Kik/Kin system and various other examples in
real life to illustrate that (i) the use of platform tokens as local media of exchange and forms
with exogenous user network.7In practice the reliability of blockchain and its commitment can be part of the platform productivity. As
analyzed by Biais, Bisiere, Bouvard, and Casamatta (2017), proof-of-work protocols can lead to competingrecords of transactions (“forks”). Saleh (2017) analyzes the forks of proof-of-stake blockchains.
8Beside newly minted tokens from platforms, decentralized contributors such as miners can also receivemarket-based compensation, as seen in the transaction fees users attach (Easley, O’Hara, and Basu, 2019;Basu, Easley, O’Hara, and Sirer, 2019; Huberman, Leshno, and Moallemi, 2019). Note that entrepreneursin most ICO models simply issue tokens to raise financing of products which they sell to earn future profit,thus do not concern the erosion of franchise value. Canidio (2018) is a rare exception and complements ourpaper in that he focuses on entrepreneurs’ effort provision before a platform launch.
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of compensation for dispersed agents is a hallmark feature of modern platforms, especially
those blockchain-based, (ii) platform designers increasingly utilize token design and supply
policy to manage platform development dynamically, (iii) platform owners derive benefit
by issuing themselves tokens and actively managing the token amount in circulation. Our
model is set up to fully capture these salient features.
Platform economy. Many of the largest companies in the world such as Alibaba, Amazon,
Apple, Facebook, Microsoft, and Tencent are all platform businesses that match dispersed
users with product/service providers, maintain digital-network infrastructures, and facilitate
third-party innovations within their ecosystems.9 The most salient and defining feature of
platform businesses is network effect (e.g., Cusumano, Yoffie, and Gawer, 2019). Beside,
digital platforms inevitably entail the concept of community/ecosystem/supply chain and
give rise to the “gig economy” wherein on-demand labor and resources from dispersed or
even anonymous agents in the network play important roles in the evolution of platforms.10
Platform businesses therefore face three critical issues: (i) The positive network external-
ity among users of a platform implies scale and first-mover advantage are crucial. Platforms
have to devote significant resources to user acquisition and retention. (ii) Platforms have
to incentivize and compensate participants to innovate and grow the system, yet bilateral
long-term employment contracts prove too costly when the participants and contributors
are too dispersed (sometimes anonymous and the participation ephemeral). (iii) Like in any
other business, platforms are firms that have to make dynamic decisions on financing and
investment in infrastructure or talent.
Trust and blockchain solution. The issues above concern not only platform owners.
Users unknown to one another have to trust the platform to conduct transactions on the
network; open source contributors and third party innovators (e.g., app developer on the
Android system) have to trust the platform that they would be fairly and timely compen-
sated; investors and key personnel for the platform have to watch out for dilution of their
9Even many traditional firms such as General Electric are exploring ways to adopt platform thinking tospeed up growth and improve performance (Cusumano, Yoffie, and Gawer, 2019).
10Uber, Handy, Upwork, and PeoplePerHour are among the thousands of platforms worldwide that emergedin recent years for freelance and short-term tasks. Digital platforms organize productive activities directlyaround their demand rather than through the intermediation of firms (Economist, 2018). Such activitiesaccount for significant portions of participating worker’s total wages (Farrell, Greig, and Hamoudi, 2018).Taking the perspectives of traditional businesses, it is hard to imagine Uber owns almost no car and Airbnbowns almost no house.
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shares and stakes in the platform.11 Traditional solutions have relied on the reputation of
centralized parties such as the platform owners. When a buyer puts her payment into an
escrow account on Taobao.com to be released to the seller once she receives the goods in
satisfactory conditions, she is placing good faith on Alibaba’s being responsible.
Blockchains present an alternative that is more decentralized. Although not always
necessarily required, a majority of blockchain applications entail the use of cryptocurrencies
and crypto-tokens. In the past few years, over 1000 different cryptocurrencies have been
introduced and many central banks are actively exploring cryptocurrency and blockchain
for retail and payment systems.12 In these payment and settlement applications including
Bitcoin and Ripple, blockchains provide decentralized consensus that helps avoiding double-
spending and enables digital currencies to act as media of exchange.
In terms of (crowd-based) financing, blockchain-based crypto tokens have also emerged
as a popular means to raise funds for startups. In Initial Coin Offerings (ICOs), Security
Token Offerings (STOs), and Initial Exchange Offerings (IEOs), entrepreneurs sell “tokens”
or “AppCoins” to dispersed investors around the globe.13 Moreover, tokens are routinely
used as compensations for talents joining the startup teams.
Overall, blockchains help enable the use of platform tokens and many recent startups
trigger interests in the economics of using tokens on general platforms, blockchain-based
or not, because designing platform tokens essentially allows businesses to have a monetary
policy tool at the firm/platform/ecosystem level.
Kik/Kin case. Kik Interative Inc. is a social media messaging company founded in Wa-
terloo in 2009 and is currently under a well-publicized lawsuit by the SEC for violations
of the Securities Act. Kik introduced a messaging app “Kik Messenger” in 2010 that later
became one of the most popular social media applications (Brenner, 2018).
11Various mechanisms for building trust such as seniority provisions, restrictive covenants, relationshipfinance, and collateralization have been introduced but are not fully satisfactory, as we discuss in Section 6.
12For example, People’s Bank of China aims to develop a digital currency system; Bank of Canada andSingapore Monetary Authority use blockchain for interbank payment systems; Deutsche Bundesbank workson prototype of blockchain-based settlement systems for financial assets; in a controversial move, the gov-ernment of Venezuela became the first federal government to issue digital currency and announced on Feb20, 2018 the presale of its “petro” cryptocurrency — an oil-backed token as a form of legal tender that canbe used to pay taxes, fees and other public needs.
13While the first ICO in 2013 raised a meager $500k and sporadic activities over the next two years.2016 saw 46 ICOs raising about $100m and according to CoinSchedule, in 2017 there were 235 Initial CoinOfferings. The year-end totals came in over $3 billion raised in ICO. In August, 2017, OmiseGO (OMG) andQtum passed a US$1 billion market cap today, according to coinmarketcap.com, to become the first ERC20tokens built on the Ethereum network and sold via an ICO to reach the unicorn status.
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To better compete with larger players in the advertising market and to allow its users
monetize their participation, Kik launched Kik Points, a virtual currency within Kik Mes-
senger in 2014. Advertisers can exchange fiat money with Kik for points to pay consumers
for answering surveys and polls and consumers can pay for purchases and usage with the
points. Kik Points while in operation created an average of 300,000 daily transactions, but
advertisers and users are concerned that nothing prevents Kik from creating more Kik Points
or stopping accepting them entirely in future.
The company therefore introduced a new blockchain-based platform, Kin, which issues
native tokens for user transactions and compensations for dispersed contributors in an ecosys-
tem for digital services and social network wherein Kik is a key founding member.14 The
Kin project is overseen by the Kin foundation and aims to offer Kik and similar develop-
ers a way to monetize their businesses which was previously difficult without large initial
scale or abusing user data. Because the blockchain-based token can guarantee a fixed sup-
ply and goes beyound Kik Messenger to include unlimited number of applications, services,
products from unlimited number of developers, Kin has the potential to overcome the di-
lution/inflation issue and the hazard of a single entity (such as Kik) destroying its value
completely.
Importantly, even though the supply of Kin is capped at $10 trillion USD, the founding
team and the Kin Foundation actively manage the dynamic token allocations (e.g., using
smart contracts): 30% is pre-allocated to the original Kik platform for being a founding
member of Kin and early adopter, 10% (1 trillion) of Kin tokens are issued to dispersed in-
vestors in a 2-week initial coin offering (ICO), raising about US$100 million, 60% is initially
allocated to the Kin foundation and is to be gradually distributed to early users and con-
tributors through the Kin Rewards Engine schema or used to cover operation and marketing
expenses. Every year, 20% of the remaining token reserves at the Kin Foundation is released
to corporate partners to be used, for example, as incentive payments. While it is unclear if
Kik and Kin optimally designed the allocation, they apparently thought about issues related
to promoting user adoption, incentivizing third-party contributors to the system, controlling
inflation, and compensating key personnel and partners while growing the platform.15
The case of Kik/Kin leads to the following three observations that apply generally to
(blockchain-based) platforms.
14Facebook’s role in the creation of Libra coins is similar.15Interested readers can find out more at, e.g., https://www.reddit.com/r/KinFoundation/comments
/8r2ull/circulatingsupplyandallocation/andhttps : //blog.usejournal.com/kins − 10 − trillion − supply −and− the− case− for − kinnies− a41e2037c64c.
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(i) Token embedding. It should be clear from the Kik/Kin case that tokens are used as
a platform currency/local medium of exchange — the “Token Embedding” phenomenon first
highlighted in Cong, Li, and Wang (2018). Indeed, in many existing blockchain applications,
native tokens are the required or favored medium of exchange.16 For example, it is cheaper to
make international payments and settlements using Ripples (RXP) on the Ripple network;
to make profit by providing validation services, OmiseGo (OMG) tokens are required as
stakes on the OmiseGo blockchain; even though Ethereum platform allows other AppCoins
and cryptocurrencies, many transactions and fundraising activities are still carried out using
Ethers (ETH) because of the convenience and popularity. Moreover, platform owners actively
design the rules for token supplies and attributes and use tokens to compensate investors
and contributors as well as to manage the platform development.
We note that it is natural and common in practice to introduce platform tokens that
agents hold and use because transfers in fiat currencies inevitably rely on centralized third
parties such as banks that are subject to the confines of physical location and jurisdictions.
Tokens, in contrast, can be used not only for peer-to-peer exchanges, but also for compen-
sating miners, validators, and other contributors who work to improve the stability and
functionality of the ecosystem. This is especially convenient because cryptocurrency miners
who maintain network securities under PoWs and liquidity providers in a staking-based sys-
tem are not long-term employees of the platform and demand on spot, reliable payments.
Moreover, native coins can be directly linked to history of transactions and events on the
blockchain, a feature other currencies cannot provide.17
One example is Filecoin (FIL) which is used as the sole means of payment in the network
marketplace to reward miners for block creation in the Filecoin consensus process. Another
example is Basic Attention Token (BAT). As Strategic Coin explains in its BAT token
launch research report, also functions as a medium exchange between users, advertisers,
16See also Brunnermeier, James, and Landau (2019) who conclude, “Payments are at the center of anyeconomic platform, and all other activities would organize themselves around the central payment func-tionality.” Even though policy makers sometimes generically refer to non-cash-flow-based tokens as “utilitytokens,” we note that the majority of them are not for redeeming a product or service from the platformowner per se at fixed price. They represent the right to use the platforms to conduct business. These includemany of the highest-profile projects: Filecoin, Golem, 0x, Civic, Raiden, Basic Attention Token (BAT), andmore. Prices are not pre-set but derive from market interactions. On the Kin platform, for example, sellersand buyers set prices themselves.
17Kocherlakota (1998) treats money as an object that does not enter utility or production functions, andis available in fixed supply. He then shows that from a technological point of view, money is equivalent toa primitive form of memory. Now with the blockchain technology, money is indeed memory. The coins canindeed be associated with the knowledge of the full histories of the agents the one of them has direct orindirect contact with.
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and publishers who participate in the Brave browser ecosystem. Advertisers purchase ads
using BAT tokens, which are then distributed among both publishers and browser users as
compensation for hosting the ads and viewing them, respectively.
The fact that (blockchain-based) platform ecosystems tend to be mediated by native
tokens is only one aspect of token embedding. In principle no one needs to hold the native
token if its velocity is infinite, i.e., people can instantaneously exchange other currencies with
the native tokens. The second aspect of token embedding is that agents actually need to
hold the tokens to conduct transactions and perform economic activities. While this is also
true for fiat money in practice, blockchain-based systems add at least three more reasons.
First, to incentivize and allocate service flows to decentralized miners or service providers,
many tokens are designed such that these agents have to hold the native tokens to earn the
right to perform work to maintain the system, be it service provision or recordkeeping. Proof-
of-Stake protocols typically fall in this category. These tokens are sometimes referred to as
work tokens or staking tokens, and notable implementations include Keep (off-chain private
computation), Filecoin (distributed file storage), Truebit (off-chain computation), Livepeer
(distributed video encoding), and Gems (decentralized mechanical Turk).18
Second, blockchains enable the use of smart contracts—digital contracts allowing terms
contingent on decentralized consensus that are typically self-enforcing and tamper-proof
through automated execution. Smart contracts need to automate transactions once certain
contingencies are fulfilled, which in turn requires a certain amount of tokens to be “escrowed”
during the episode that such contingencies may be triggered.
Third, because the generation of decentralized consensus takes time, there is a technical
limit on how quickly transactions can be validated and recorded. While many protocols such
as the Lightening Network and Ethereum process transactions significantly faster than Bit-
coin (seconds versus 10-11 minutes), the decentralized nature of the validation means it takes
time to ensure robustness and synchronization of the consensus. During the confirmation
period, agents have to hold tokens.
(ii) Dynamic token supply and platform management. Admittedly, much of the
discussion on cryptocurrency has focused on its role as a competitor for fiat currency for
18To enforce a mechanism to penalize workers who fail to perform their job to some pre-specified standard,work tokens have to be held as collateral. For example, in Filecoin, service providers contractually committo storing some data with 24/7 access and some minimum bandwidth guarantee for a specified period oftime. During the contract term, service providers must “escrow” some number of Filecoin, which can beautomatically slashed (taken away) should they fail to perform the service.
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general payments. In a way, fiat currencies are also an extreme form of platform tokens in
that people “join” the platform by recognizing their value and accepting them (Gans and
Halaburda, 2015), and the platform being the broader economy. What distinguishes tokens
on digital platforms is that the adoption is no longer dictated by physical constraints: it
is way more costly to adopt a different fiat currency by emigrating to a different country,
but switching among digital platforms are relatively easy, which implies that the adoption
of digital platforms are more endogenous than the adoption of a fiat currency.
Not only user adoption on platforms is endogenous, the development of platforms is also
endogenous. Just like executives manage firms’ hiring and investment dynamically, tokens
allow platform owners to manage the contributions from dispersed agents in the network
and thus the evolution of the platform. It is not only about a one-time ICO.
For example, Kin tokens were issued to allow broad adoption and contribution by de-
velopers and users to foster a “virtuous cycle in which the ecosystem grows in both size
and quality” (Livingston, 2017). Through measures such as capping individual purchases at
$4,400, Kik structured the offering to encourage actual usage of the tokens as a medium of
exchange instead of speculation. It is believed that an entire ecosystem of independent users
and developers would have the right incentives to grow the platform. Indeed, by the end
of 2018, Kin exceeded Ether and Bitcoin in blockchain user activities according to blocktiv-
ity.info. Both the Apple App and Google Play Stores accept Kin as a digital currency; the
Kin ecosystem has also integrated dozens of third-party apps including Perfect 365, a top-
rated AR beauty app with over 100 million users, and Nearby, a popular app with millions
of users for meeting new people. The Kin Rewards Engine schema dynamically incentive
agents in the system to grow the platform.
We should remind the readers that the use of platform tokens are not necessarily decen-
tralized or blockchain-based. Even a traditional, centralized transaction platform may see
the opportunity to create open interfaces - APIs (e.g., Uber have opened up APIs to enable
third parties to add value) and use platform tokens. Kik was using local currency even
though it was not blockchain-based; many community-based companies such as Facebook
and Tencent, Microsoft, and Amazon have also introduced platform tokens before (see Gans
and Halaburda (2015) for an excellent discussion). Other notable examples include Linden
dollar for the game Second Life, WoW Gold for the game World of Warcraft. Gans and
Halaburda (2015) and Halaburda and Sarvary (2016) provide excellent early discourses on
virtual currencies on platforms.
What is different about blockchain-based platforms is that the distributed ledger tech-
12
nology brings immutability and decentralized consensus to enable smart contracting, which
potentially allows commitment from the platform designers not seen before and not reliant
on reputation alone.
(iii) Entrepreneurs’ token dividends. How entrepreneurs get compensated through
tokens is under-discussed in academic studies yet is important in practice. As seen in the
Kik/Kin example, founders, early investors, key personnel get tokens which they can offload
in secondary markets for consumption. This is a form of seigniorage.19 What distinguishes
blockchain-based platforms is that the issuance of tokens can be rule-based whereas inflation
presents a perennial concern with fiat money and central banks. Indeed, many token designs
specifically guard against inflation, for example, by capping the token supply. Bitcoin supply
is capped at 21 million and Dfinity, at 469.21 million. Platforms like Kin also employs a
token supply policy that targets at optimally incentivizing innovative proposals and growing
the platform, as well as compensating the owners.
Precisely because tokens are used to compensate platform owners, entrepreneurs and
token designers care about how “inflated” the ecosystem is because they care about the
platform’s franchise value going forward. This leads to many platforms also burning tokens
to reduce inflation. Kin burned about 10% of tokens during the migration from Etheorem to
its own blockchain.20 Another recent example of discretionary reduction of token in supply
is the Synereo team which burned 33% of its cryptocurrency reserves on March 31, 2018
after meeting development goals with fewer tokens (AMP) than initially project.21
3 Model
There are three types of agents in a continuous-time economy: an entrepreneur represent-
ing platform owners, a pool of competitive contributors, and a unit measure of users. The
owner designs the platform’s protocol. Contributors devote efforts and resources required
for the operation and continuing development of the platform. Users conduct peer-to-peer
transactions and realize trade surpluses on the platform. A generic consumption good serves
19Entrepreneurs earn seigniorage for building infrastructure for and promoting platform networks. Evenfor stablecoins such as JPM Coin and Libra, the core networks of powerful institutions the founders fosteradd to attracting users. Key members in Libra are also compensated through Libra Investment Tokens.
20https://medium.com/kinblog/blockchain-strategy-update-next-steps-in-migrating-to-the-kin-blockchain-aed99e209654
21https://synereo.com/burn-amps/
13
as the numeraire. We first lay out the economic environment of the platform in question.
3.1 Platform Productivity and Contributors
We study a dynamically evolving platform whose productivity (quality), At, evolves as
dAtAt
= LtdHt, (1)
where Lt is the resources invested into productivity growth by the platform and dHt is a
shock to investment efficiency
dHt = µHdt+ σHdZt. (2)
Here Zt is a standard Brownian motion that generates the information filtration of this
economy. The platform productivity At broadly captures platform matching technologies,
network security, processing capacity, regulatory conditions, users’ interests, the variety of
activities feasible on the platform, etc. It therefore affects directly users’ utility on the
platform, which shall be made clear shortly. We consider a stochastic economy because we
want to explore the model’s implications on the volatility of token price.
Platform productivity grows through Lt, which may represent labor or capital inputs.
Blockchain-based platforms often pay workers or investors on the spot with their tokens
instead of a contract that promises the typical deferred compensation. Note that even in
the simplest setting of production where firms combine labor and capital into output (often
through a Cobb-Douglas function), there exists an implicit assumption that firms obtain
inputs and then pay workers and investors the after production. The role of tokens as means
of spot payment is especially salient on blockchain-based platforms.
Our focus is on the dynamic interaction between the entrepreneur and platform users,
so we do not explicitly model contributors’ decision-making but instead specify directly the
required numeraire value of payment for Lt to be F (Lt, At), which is increasing and convex
in Lt and may also depend on At. Let Pt denote the unit price of token in terms of the
numeraire (consumption goods). Given At, to gather the resources Lt, the platform issues
F (Lt, At) /Pt units of new tokens to workers.
Let Mt denote the total amount of circulating tokens (i.e., token supply). The payment
for Lt leads to new issuance that adds to the growth of token supply, dMt, by F (Lt, At) /Pt.
The functional form of F (·) depends on the structure of labor or capital markets that a
14
typical blockchain-based platform participates in. A distinguishing feature of labor supply
in a “gig economy” is that workers provide on-demand contributions and receive token pay-
ments instead of long-term employment contracts.22 Here tokens facilitate the acquisition
of labor by allowing the platform to pay for labor on the spot and thereby avoiding the
limited commitment on the part of platform that arises in the implementation of deferred
compensation and may lead to complex legal enforcement issues especially when workers
and the platform belong to different judicial areas. Moreover, since digital tokens are often
programmable (via smart contracting), escrow accounts can be set up and enforced automat-
ically so that tokens are released to workers only if their inputs (e.g., programming codes)
are received. Therefore, tokens also reduce the platform’s exposure to workers’ limited com-
mitment.23 Finally, Lt also represents the capital received from crowd-based investors, for
example through initial coin offerings (ICOs) or seasoned token offerings (STOs). Investors
receive tokens immediately on the spot instead a promise of payoff in the future, and thus,
avoid exposure to the platform’s failure to deliver future returns.24
A new issue emerges – workers and investors who receive tokens as compensation may still
worry about token depreciation because the platform may issue more tokens in the future.
In other words, while tokens avoid limited commitments by facilitating spot payments, the
platform’s lack of commitment against excess token supply is still a concern. Our analysis
of optimal token supply addresses this question, but first let us introduce platform users.
3.2 Platform Users
In our model, after receiving tokens, workers and investors may immediately sell tokens
to users. Workers and investors who contribute Lt can also be users themselves, and the
model is not changed at all as long as the utility from token usage and the disutility from
contributing Lt (which gives rise to F (·)) are additively separable.
As in Cong, Li, and Wang (2018), users can conduct transactions by holding tokens. We
use xi,t to denote the value (real balance) of agent i’s holdings in the unit of numeraire. By
22Workers may represent miners in Proof-of-Work-based public blockchains or drivers on ride-sharing apps.23Another reason to introduce tokens as means of payment for Lt is the heterogeneity in labor quality.
Consider a subset of workers supply high-quality efforts because they understand better the technologiesbehind the platform. Naturally, these capable workers assign a higher value to tokens because they are notconcerned about the adverse selection problem that low-quality workers face due to their lack of technologicalknowledge. In other words, in contrast to cash-based compensation, token-based compensation screens outhigh-type workers and thereby improves the match between employer (the platform) and employees (workers).
24In general, blockchain-based tokens have immutable transaction recording that finalizes the digital trans-actions among dispersed, untrusted agents.
15
facilitating transactions, these holdings generate a flow of utility (or convenience yield) over
dt given by
x1−αi,t (Nγt Atui)
α dt, (3)
where Nt is the platform user base, ui captures agent i’s idiosyncratic needs for platform
transactions, and α, γ ∈ (0, 1) are constants. We provide a theoretical foundation for this
specification of transaction surplus in Appendix A. A crucial difference from Cong, Li, and
Wang (2018) is that we endogenize At and the token supply Mt.
The flow utility of token holdings depends on Nt, the total measure of users on the plat-
form with xi,t > 0.25 This specification captures the network externality among users, such
as the greater ease of finding trading or contracting counterparties in a larger community.
We assume that users’ transaction needs, ui, are heterogeneous. Let Gt (u) and gt (u)
denote the cross-sectional cumulative distribution and density functions respectively that are
continuously differentiable over a support [U t, U t] and may vary over time. ui can be broadly
interpreted. For payment blockchains (e.g., Ripple and Bitcoin), a high value of ui reflects
user i’s needs for international remittance. For smart-contracting platforms (e.g., Ethereum),
ui captures user i’s project productivity, and token holdings facilitate contracting.26 For
decentralized computation (e.g., Dfinity) and data storage (e.g., Filecoin) applications, ui
corresponds to the need for secure and fast access to computing power and data.
As Pt denotes the unit price of token in terms of the numeraire, we let ki,t denote the
units of token that user i holds so the real balance
xi,t = Ptki,t. (4)
To join the platform (i.e., ki,t > 0), a user incurs a flow cost φdt. For example, transacting
on the platform takes effort and attention. Therefore, agents with sufficiently high ui choose
to join the platform, while agents with sufficiently low ui do not participate.
Let yi,t denote user i’s cumulative utility from platform activities. As in Cong, Li, and
Wang (2018), we assume that either the users are well-diversified so that their transaction
surpluses on the platform are priced by a stochastic discount factor. Equivalently, we can
25One is example involves a producer who accepts tokens as means of payment and earns net profits equalto the full transaction surplus. The profits depend on the scale of operation, i.e., the sales xi,t, and variablesthat determine the profit margin, which include the total outreach, Nt, the platform efficiency At, and theproducer’s idiosyncratic productivity ui.
26For example, in a debt contract, the borrower’s Ethereum can be held in an escort or “margin” account,which is automatically transferred to the lender in case of default. Posting more Ethereum as margin allowsfor larger debt contracts, which in turn lead to projects of larger scale and profits.
16
write the optimization problem under the risk-neutral measure.27 User i then maximizes
life-time utility under the risk-neutral measure,
E[∫ ∞
0
e−rtdyi,t
], (5)
where we can write the incremental utility dyi,t as follows:
dyi,t = max
{0, max
ki,t>0
[(Ptki,t)
1−α (Nγt Atui)
α dt+ ki,tEt [dPt]− φdt− Ptki,trdt]}
. (6)
The outer “max” operator in (6) reflects user i’s option to leave the platform and obtain
zero surplus, and the inner “max” operator reflects user i’s optimal choice of ki,t.
Inside the inner max operator are four terms that add up to give the incremental trans-
action surpluses from platform activities. The first term corresponds to the blockchain trade
surplus given in (3). The second term is the expected capital gains from holding ki,t units
of tokens. Users care about the sum of the on-chain transaction surplus and the expected
token appreciation given by the first two terms in (6). The third term is the participation
cost, and the last term is the financing cost of holding ki,t units of tokens.
It is worth emphasizing that on this tokenized platform, users must hold tokens for at
least an instant dt to complete transactions and derive utility flows. Section 2 contains
motiving examples and institutional details. This holding period exposes users to token
price change over dt.
3.3 The Entrepreneur
The entrepreneur represents the founding developers who own the platform and design
its protocol that includes the development strategy {Lt, t ≥ 0}. Over time, the entrepreneur
receives a cumulative number of tokens Dt as dividends and evaluates the tokens with a
risk-neutral utility function and time discount rate r:
max{Lt,Dt}t≥0
∫ +∞
t=0
E[e−rtPtdDt
[I{dDt≥0} + (1 + χ) I{dDt<0}
]]. (7)
27For the special case where users are risk neutral, the risk-neutral measure is the same as the data-generating physical measure.
17
When dDt > 0, the entrepreneur receives token dividends that have a market value Pt per
unit.28 Note that in equilibrium, the entrepreneur immediately sells her tokens to users who
derive an extra convenience yield from token holdings.
We allow the entrepreneur to buy back and burn tokens to reduce the token supply (i.e.,
dDt < 0). By reducing token supply, the owner can boost token price, and as a result,
increase the value of future token dividends. A higher token price also allows the platform to
gather more resources for productivity growth in the future. When dDt < 0, the entrepreneur
raises external financing (numeraire goods) at a proportional cost χ and buy back tokens.29
As will be shown below, introducing such financing costs creates a conflict of interest between
the entrepreneur and platform users, and thereby, allows us to discuss the role of blockchain
as commitment device and how it affects the entrepreneur and users’ welfare.
Considering both the token issued for investment Lt and the entrepreneur’s dividend/buy-
back, we have the key accounting identity that describes the evolution of token supply:
dMt =F (Lt, At)
Ptdt+ dDt. (8)
The left side relates to tokens’ function as means of payment while the right relates to financ-
ing and payouts. When the platform invests (first term of right side) or distributes token
dividends (second term of right side), the total amount of tokens in circulation increases;
the token supply decreases when the entrepreneur burns tokens out of circulation. Later we
show that the platform owner’s financial slack varies with Mt due to the financing cost χ,
so the token stock is akin to the cash inventory in Bolton, Chen, and Wang (2011), except
that the token price is endogenous and the financial slack decreases in Mt.
In what follows, we characterize a Markov equilibrium with the platform productivity At
and the token supply Mt as state variables.
Definition 1. A Markov equilibrium with state variable At and Mt is described by agents’
decisions and equilibrium token price such that the token market clearing condition holds,
users optimally decide to participate (or not) and choose token holdings, contributors supply
28For example, blockchain behemoth Bitmain Technologies Ltd and Founders Fund (known for early betson SpaceX and Airbnb) invest in EOS and hold ownership stakes that entitle them for future token rewards.The gradual distribution of token dividends can be viewed as contingent vesting in reality – a certain amountof total tokens Dt have been allocated by time t but are distributed over time (via dDt) depending on thestages of platform development and the tokens outstanding (i.e., different values of At and Mt).
29The parameter χ may also represent the forgone consumption and other investment opportunities. It isconsistent with Bolton, Chen, and Wang (2011) who also model in reduced form the information, incentive,and transactions costs that a firm incurs whenever it raises real resources from external equity market.
18
resources for the compensation of F (Lt, At) in numeraire value, and the platform strategies,
i.e., Lt and Dt, are optimally designed to maximize the owner’s value.
4 Dynamic Equilibrium
We first derive the platform owners’ optimal investment and token dividend distribution,
which in turn pin down the token supply. We then derive platform users’ optimal decisions
on adoption and token holding in order to aggregate token demand. Finally, token market
clearing yields the equilibrium dynamics of token price, decentralized contribution, user
adoption, and token allocation.
4.1 Optimal Token Supply
At time t, the owner’s continuation or franchise value Vt (i.e., the time-t value fucntion)
satisfies the following Hamilton–Jacobi–Bellman (HJB) equation
rV (Mt, At) dt = maxLt,dDt
PtdDt
[I{dDt≥0} + (1 + χ) I{dDt<0}
]+ VMt
[F (Lt, At)
Ptdt+ dDt
](9)
+ VAtAtLtµHdt+
1
2VAtAtA
2tL
2t (σ
H)2dt.
The first term in this HJB equation reflects the platform’s dividend payout (dDt > 0)
and buyback (dDt < 0). When there are more tokens circulating, the token price tends to be
low, and so does the owner’s continuation value. Therefore, we expect VMt < 0, as we later
confirm in the numerical solution. Payout occurs only if −VMt ≤ Pt, i.e., the marginal cost
of increasing token supply is not greater than the market value of token. Buyback happens
when −VMt ≥ Pt (1 + χ), i.e., when the marginal benefit of decreasing token supply is not
less than the cost of burning tokens. The second term is the product of marginal value of
token supply, VMt , and the drift of token supply, which consists of tokens paid to contributors
and tokens distributed to or burned by the entrepreneur. The third term is the marginal
benefit of an At increase. The platform productivity increases in labor Lt, which is the mean
productivity of AtµHdt. But hiring labor using tokens increases the token supply Mt, which
has a marginal cost of VMt
FLtPtdt as VMt < 0. Moreover, labor productivity is uncertain, so
the fourth term captures how such risk enters into the choice of Lt. The next proposition
summarizes the platform’s optimal policies.
19
Proposition 1 (Optimal Token Supply). The optimal token supply strategy is given by
(1) the optimal choice of Lt solved implicitly by the following equation
VAtAtµH + VAtAtA
2tL∗t
(σH)2
= FL (L∗t , At)
(−VMt
Pt
)(10)
and (2) the optimal choice of dDt — the owner receives token dividends (dD∗t > 0) only if
Pt ≥ −VMt, and buys back and burns tokens out of circulation (dD∗t < 0) only if −VMt ≥Pt (1 + χ).
Equation (10) equates the marginal benefit of investment to the marginal cost. The left
side is the marginal impact on the drift of At, evaluated by the entrepreneur’s marginal value
of At growth and adjusted for the risk of productivity shock via the second term.
The right side is the marginal cost of investment. Since the entrepreneur’s marginal cost
of token supply can be larger than the market value of tokens, the physical marginal cost FL
is multiplied by −VMt/Pt. This multiplier reflects a token issuance cost. Here the platform
pays for investment with “undervalued” tokens. The payout/buy-back policy in Proposition
1 implies that VMt/Pt ∈ [1, 1 + χ]. Because the entrepreneur incurs a financing cost χ > 0
when burning tokens, there exists a region of (Mt, At) such that VMt/Pt > 1, i.e., a token
issuance cost exists. As will be shown in the solution, the condition −VMt ≥ Pt holds in
strict inequality almost everywhere. We have the following corollary that highlights the link
between off-platform capital markets and the platform’s token issuance cost.
Corollary 1 (Token Issuance Cost). The entrepreneur’s off-platform financing cost χ
leads to a token issuance cost: When χ > 0, there exists a positive measure of (Mt, At) such
that the token issuance cost is positive, i.e., −VMt/Pt > 1. This issuance cost distorts the
investment policy by amplifying the marginal cost of investment as shown in Equation (10).
Our characterization of the optimal payout/buyback policy allays the concern over fraud-
ulent designs by founding developers and the resulting explosion of token supply that destroys
token value. One might worry that the entrepreneur has strong incentive and ample oppor-
tunity to build “back doors” in the protocol that allow them to steal tokens when tokens
become valuable. The stolen tokens are likely to be sold in secondary markets for dollars,
and thus, depress the token price. However, as shown in Proposition 1, our setup already
allows the entrepreneur to extract token as dividends and the optimal payout policy maxi-
mizes the owner’s value, so it is an incentive-compatible rewarding scheme for the founding
designers. In other words, we characterize a subgame perfect equilibrium between a large
20
layer (the platform) and a continuum of small players (users). From a regulatory perspec-
tive, any proposal of blockchain or platform design should disclose the payout schemes to
the founding developers and they should be broadly inline with the above characterization.
Corollary 2 (Resistance Against Excess Token Supply). By Pontryagin’s maximum
principle, the optimal payout and investment policies in Proposition 1 maximize the en-
trepreneur’s value at any t and rule out excess token supply from additional token issuance.
4.2 Optimal Token Demand
We conjecture and later verify that in equilibrium, the token price, Pt, evolves as
dPt = PtµPt dt+ Ptσ
Pt dZt, (11)
where µPt and σPt are endogenously determined. Agents take the price process as given under
rational expectation. Conditioning on joining the platform, user i chooses the optimal token
holdings, k∗i,t, by using the first order condition,
(1− α)
(Nγt AtuiPtk∗i,t
)α+ µPt = r, (12)
which states that the sum of marginal transaction surplus on the platform and the expected
token price change is equal to the required rate of return, r.
Rearranging this equation, we obtain the following expression for the optimal token
holdings:
k∗i,t =Nγt AtuiPt
(1− αr − µPt
) 1α
. (13)
k∗i,t has several properties. First, agents hold more tokens when the common productivity,
At, or agent-specific transaction need, ui, is high, and also when the user base, Nt, is larger
because it is easier to conduct trades on the platform. Equation (13) reflects an investment
motive to hold tokens, that is k∗i,t increases in the expected token appreciation, µPt .
Using k∗i,t, we obtain the following expression for the user’s maximized profits conditional
on participating on the platform:
Nγt Atuiα
(1− αr − µPt
) 1−αα
− φ. (14)
21
User i only participates when the preceding expression is non-negative. That is, only those
users with sufficiently large ui participate. Let ut denote the type of the marginal participant,
then
ut = u(Nt;At, µ
Pt
)=
φ
Nγt Atα
(r − µPt1− α
) 1−αα
. (15)
The adoption threshold ut is decreasing in At because a more productive platform attracts
more users. The threshold also decreases when agents expect a higher token price appreci-
ation (i.e., higher µPt ). Because only agents with ui ≥ ut participate, the user base is then
Nt = 1−Gt (ut) . (16)
Equations (15) and (16) jointly determine the user base Nt given At and µPt . Note that zero
adoption is always a solution, and trivially leads to zero token price.
Proposition 2 (Token Demand and User Base). Given At and µPt , the platform has
a positive user base if Equations (15) and (16) have solutions for ut and Nt. Conditional
on participating, User i’s optimal token holding, k∗i,t, is given by Equation (13). The token
holding, k∗i,t, decreases in Pt and increases in At, µPt , ui, and Nt.
To obtain the numerical solution, we later specify Gt (u) and explicitly derive Nt.
4.3 Token Market Clearing
Clearing the token market determines the token price. Let us define the participants’
aggregate transaction need as
Ut :=
∫u≥ut
ugt (u) du, (17)
the integral of ui of participating agents.
The market clearing condition is
Mt =
∫i∈[0,1]
k∗i,tdi. (18)
Substituting optimal holdings in Equation (13) into the market clearing condition in Equa-
tion (18), we arrive at the Token Pricing Formula.
22
Proposition 3 (Token Pricing). The equilibrium token price is given by
Pt =Nγt UtAtMt
(1− αr − µPt
) 1α
. (19)
The token price increases in Nt – the larger the user base is, the higher trade surplus
individual participants can realize by holding tokens, and stronger the token demand. The
price-to-user base ratio increases in the platform productivity, the expected price appreci-
ation, and the network participants’ aggregate transaction need, while it decreases in the
token supply Mt.30 Equation (19) implies a differential equation for Pt on the state space
of (Mt, At). This can be clearly seen once we apply the infinitesimal generator to the token
price, Pt = P (Mt, At), in the Markov equilibrium to express µPt into a collection of first and
second derivatives of Pt by Ito’s lemma. Note that the equilibrium user base, Nt, is already a
function of At and µPt as shown in Proposition (2). Therefore, the collection of token market
clearing condition at every t essentially solve the full dynamics of token price.
Together, Equation (8) and (18) describe the primary and secondary token markets. The
change of Mt is a flow variable, given by Equation (8), that includes the new issuances from
platform investment and payout and the repurchases by the entrepreneur. The token supply
Mt is a stock variable, and through Equation (18), it equals the token demand of users.
5 Equilibrium Characterization
We further characterize the equilibrium by analytically deriving and numerically solv-
ing the system of differential equations concerning token price and platform owners’ value
function. To streamline exposition and focus on core economic insights, we make some
simplifying parametric assumptions.
30The formula reflects certain observations by practitioners, such as incorporating DAA (daily activeaddresses) and NVT Ratio (market cap to daily transaction volume) in token valuation framework, butinstead of heuristically aggregating such inputs into a pricing formula, we solve both token pricing and useradoption as an equilibrium outcome. See, for example, Today’s Crypto Asset Valuation Frameworks byAshley Lannquist at Blockchain at Berkeley and Haas FinTech.
23
5.1 Parametric Choices
Following the literature on investment in finance and macroeconomics (e.g., Bolton, Chen,
and Wang, 2011), we assume a convex (quadratic) investment cost function of F :
F (Lt, At) =
(Lt +
θ
2L2t
)At, (20)
where θ > 0 can depend on the elasticity of labor and capital supply. In comparison with tra-
ditional contracts, token-based compensation may enlarge the supply elasticity and thereby
reduce θ by alleviating the problem of limited commitment as previously discussed.
Lemma 1 (Parameterized Optimal Investment). Under the parametric restriction
given by Equation (20), the platform’s optimal investment is
L∗t =VAtµ
H +VMtPt
−VMtPtθ − VAtAtAtσ2
, (21)
To obtain closed-form solutions, we assume that ui follows the commonly used Pareto
distribution on [U t,+∞) with cumulative probability function (c.d.f.) given by
Gt (u) = 1−(U t
u
)ξ, (22)
where ξ ∈ (1, 1/γ) and U t = 1/ (ωAκt ) , ω > 0, κ ∈ (0, 1). The cross-section mean of ui isξUtξ−1 .
Note that U t decreases in At, which reflects the competition from alternative platforms
that are inspired by the platform’s success (i.e., a high value of At). For example, this
specification captures the reality that after the success of Bitcoin, alternative blockchains
emerge as competitors in the area of payments. Similarly, there now exists alternative
platforms to Ethereum for smart contracting. The effects of competition are small when ω
is close to zero. As At increases, the mass of ui is being shifted towards lower values.31
Lemma 2 (Parameterized User Base). Given At and µPt , from Proposition 2, we have
a unique non-degenerate solution, Nt, for Equations (15) and (16) under the Pareto distri-
31Platform competition can also be captured by the depreciation of At. The current specification lendstechnical convenience.
24
bution of ui given by Equation (22):
Nt =
(A1−κt α
ωφ
) ξ1−ξγ
(1− αr − µPt
)( ξ1−ξγ )( 1−α
α ), (23)
if ut ≥ 1ωAκt
, i.e., A1−κt ( 1−α
r−µPt)1−αα ≤ ωφ
α; otherwise, Nt = 1.
Our later discussion focuses on ξγ < 1 so that the user base, Nt, is increasing in the
platform productivity in spite of the competition effects. This is realistic because a technol-
ogy leader usually benefits from its innovation despite the presence of potential competing
followers. Moreover, we focus on low values of At such that Nt < 1 in the Markov equilibrium
so as to examine how token allocation interacts with user base dynamics. Under the Pareto
distribution, the aggregate transaction need is given by
Ut = Nt
(ξutξ − 1
)=
(ξ
(ξ − 1)ωAκt
)(A1−κt α
ωφ
) ξ−11−ξγ
(1− αr − µPt
)( ξ−11−ξγ )( 1−α
α ). (24)
We adopt the following parameter restriction, which helps reduce the dimension of state
space in our numerical analysis and convey economic intuitions.
Assumption 1. 2ξ−11−ξγ = κ
1−κ .
The assumption implies κ > 1/2 given that γ > 0 and ξγ < 1. Moreover, Nt increases in
At while Ut decreases in At, and the effects of At on Nt and Ut exactly cancel out each other
in the token pricing formula (Equation (19)). The intuition is that even though a better
platform productivity induces more users, individual users’ needs are now weaker because
they have access to alternative platforms. The token pricing formula then simplifies.
Lemma 3 (Parameterized Token Price). Under Assumption 1, the equilibrium token
price in Proposition 3 when Nt < 1 is given by
Pt =AtMt
ξ
(ξ − 1)ω1
1−κ
(α
φ
) κ1−κ(
1− αr − µPt
) 1α+( 1−α
α )( κ1−κ)
. (25)
In the following, we characterize a Markov equilibrium in a transformed state space. The
equilibrium variables depend on (mt, At), where
mt =Mt
At. (26)
25
By inspecting Equation (25), we can see that mt is the only state variable driving the token
price – in such an equilibrium µPt is a function of mt only and so does Pt.
For the parameters that affect user activities, we follow Cong, Li, and Wang (2018) to set
α = 0.3, φ = 1, r = 0.05, and the volatility parameter, σH = 2. For the mean productivity
growth, we set µH = 0.5, which generates a µPt in line with the values in Cong, Li, and
Wang (2018). We set the rest of parameters to illustrate the qualitative implications of the
model: θ = 10, 000 so the highest level of investment, Lt, is about 25% higher than the
lowest level; ξ = 2, κ = 0.8 and ω = 100 for the distribution parameters of ui; χ = 20%
for the financing cost. The model’s qualitative implications are robust to the choice of these
parameters. Finally, we set γ = 1/8 to satisfy Assumption 1.
5.2 Solving the Equilibrium
We numerically solve the model in the space (mt = Mt/At, At) instead of the original
space (Mt, At), because given the parametric choices in Section 5.1, mt shall be the only
state variable driving the token price Pt and the platform investment Lt. By Ito’s Lemma,
the dynamics of mt is given by
dmt
mt
=dMt
Mt
− dAtAt
+ L2t (σ
H)2dt, (27)
where the last term is a quadratic variation term from Ito’s calculus. We conjecture that
the value function V (Mt, At) = v(Mt
At
)At, so the derivatives are given by
VMt = v′ (mt) , VAt = v (mt)− v′ (mt)mt, VAtAt = v′′ (mt)m2t
At. (28)
In the interior region (dDt = 0), the HJB equation is
rv (mt) = maxLt
v′ (mt)
(Lt + θ
2L2t
)Pt
+ [v (mt)− v′ (mt)mt]LtµH +
1
2v′′ (mt)m
2tL
2t (σ
H)2. (29)
Therefore, if Pt and Lt are all functions of mt, and we confirm the value function conjecture.
Substituting these derivatives of V (Mt, At) into the optimal investment, we have
L∗t =[v (mt)− v′ (mt)mt]µ
H + v′(mt)Pt
−v′(mt)Pt
θ − v′′ (mt)m2t (σH)2
. (30)
26
Therefore, Lt is a function of mt as long as Pt is a function of mt. Equation (25) implies that
Pt is a function of mt because when Pt is a function of mt, so is µPt . Hence the conjecture of
mt being the only the state variable driving Pt and Lt is internally consistent.
The optimality conditions for dDt give us the boundary conditions to solve v (mt). We
conjecture that v′ < 0 because when mt increases, more tokens are supplied and the current
and future token price declines, which reduces the owner’s continuation value. There exists
a lower bound for mt such that mt ≥ m, dD∗t ≥ 0. At this payout boundary, the marginal
value of retained token must be equal to the market value, i.e.,
−v′ (m) = P (m) . (31)
Since the payout boundary is optimally chosen, we also have the usual “super contact”
condition:
−v′′ (m) = P ′ (m) . (32)
Moreover, because the payout boundary is a reflecting boundary, to rule out arbitrage in the
token market, we have:
P ′ (m) = 0. (33)
Intuitively, the distribution of token dividends happens when the token supply is sufficiently
small relative to the platform productivity, i.e., low mt.
The upper bound for mt is the buyback boundary. As mt increases, the token supply is
large relative to the platform productivity, and the token price declines, so the owners buy
back and burn tokens out of circulation. At mt = m,
−v′ (m) = P (m) (1 + χ) . (34)
Since the buyback boundary is optimally chosen, we also have the “super contact” condition:
−v′′ (m) = P ′ (m) (1 + χ) . (35)
Moreover, because the payout boundary is a reflecting boundary, to rule out arbitrage in the
token market, we have:
P ′ (m) = 0. (36)
At the boundaries, the amount of payout and buyback exactly offsets the variation in mt
27
from Lt and the shock dZt that would otherwise drive it beyond the boundaries.
Proposition 4 (Markov Equilibrium Solution). With Lemmas 1, 2, and 3, there exists
a Markov equilibrium with At and mt = Mt/At as state variables and the following properties:
(i) The token price P (mt) and the value function V (Mt, At) = v (mt)At uniquely solve the
system of ordinary differential equations given by Equation (25) and (29) subject to boundary
conditions given by Equations (31) to (36).
(ii) The token price Pt, platform investment Lt in Equation (30), and the payout/buy-back
policy Dt, all depend on mt only.
(iii) Users’ optimal token holdings and participation decisions together with the user base
depend on both mt and At according to Proposition 2.
Discussion: Token Supply Limit. Blockchain platforms often feature a cap on token
supply. One way to incorporate this is to have an absorbing upper bound of mt, say m.
In such case, once reaching a multiple of the platform productivity, i.e., mAt, the supply
would grow proportionally with At forever, and according to Lemma 3, token price will then
be a constant. As for newly issued tokens, they are divided between the entrepreneur and
contributors, and here the entrepreneur faces a standard consumption-savings trade-off – if
she takes a larger share of the new tokens, the productivity grows slower.
5.3 Endogenous Platform Development
Panel A of Figure 1 plots v (mt). Because the value function, V (Mt, At) = v (mt)At,
Panel A shows that the platform owner’s value, scaled by productivity, declines in the
productivity-adjusted token supply (a form of platform “inflation”). Intuitively, when more
tokens are circulating relative to platform productivity, it is more likely for the owner to
reach the buyback (upper) boundary and pay the financing cost, and in the less likely event
of token payout, the owner receives a lower value due to the depressed token price when
mt is high. Note that the value function is always positive in Panel A, suggesting that the
platform owner never abandons the platform. The curve starts at the payout boundary and
ends at the buyback boundary where the owner actively devotes real resources to buy back
and burn tokens out of circulation in order to support token price and her franchise value.
Panel B of Figure 1 plots the optimal platform investment against the productivity-
adjusted token supply. The declining pattern is largely driven by the rising cost of token
28
Figure 1: Optimal Platform Investment Financed by Token Issuances.
issuance (Panel C), even though as mt increases, the marginal value of productivity enhance-
ment rises (Panel D). The optimal L∗t increases in VAt
The optimal L∗t increases in −VMt/Pt, the ratio of the marginal cost of token issuance,
−VMt , to the token market price, Pt. This ratio measures the valuation gap that exists
between platform owners (insiders) and the workers and users (outsiders), i.e., the token
issuance cost. When the gap is high, it is costly from the owners’ perspective to gather
resources using tokens. The ratio starts at one, as implied by the value-matching condition
of the payout boundary. The gap widens as the token supply outpaces the growth of plat-
form productivity, i.e., as mt increases, and eventually, when the gap reaches (1 + χ), the
platform owner’s optimal buy back tokens. The increasing −VMt/Pt largely contributes to
the decreasing pattern of L∗t .
The optimal L∗t increases in VAt , the marginal value of At, because on average, investment
has a positive productivity, i.e., µH > 0, more resources gather by token payments, Lt, means
a higher expected growth of At. Near the buyback boundary, VAt is high because an increase
29
of At reduces mt and the likelihood of costly buyback.
Finally, according to Equation (10), the second-order derivative of value function to pro-
ductivity also affects the choice of investment, which essentially represents a precautionary
motive in the choice of Lt. It is not plotted because under the current parameterization, its
quantitative contribution to the dynamics of Lt is small. However, the intuition of precaution
towards investment risk is still interesting. The token distribution is largely a real-option
decision. While it is not completely irreversible, reversing it (i.e., buying back tokens) incurs
a cost of χ.32 The probability of incurring such costs increases as mt approaches the buy-
back boundary, so the platform becomes increasingly cautious on making large investment
that also brings in large exposure to investment productivity shock in Equation (2). There-
fore, the platform owner may choose to invest less in order to preserve some slack, i,e., the
flexibility to issue more tokens in the future.
Overall, our model reveals a rich set of trade-offs in the choice of token-compensated
contributions for platform development. The model has the potential to explain various
features of token distribution to open-source engineers, miners (ledger maintainers), and
crowd-sourced financiers in real life.
5.4 Token Price and User Adoption
The dynamics of token price is directly linked to that of token supply. As shown in
Panel A of Figure 2, the token price, Pt, declines in mt, the productivity-adjusted token
supply. From Equation (27), the diffusion of mt is −mtL∗tσ
H (through −dAt/At), which is
negative. Therefore, a positive shock in labor productivity decreases mt by increasing At,
moving the economy closer to the payout boundary. The token price increases in response
and is procyclical with respect to the shock.
That said, in stark contrast to the 200% per annum volatility of labor productivity that
we input, i.e., the fundamental volatility, σPt is surprisingly small (below 0.2% in Panel B
of Figure 2) due to the stabilizing effect of the endogenous cumulative token process Dt.
The platform owners’ incentive to pay out when mt is low and buy back when mt is high
moderate the variation of token price through the control over token supply.
Corollary 3. From Proposition 1, the token price is bounded in[−(
11+χ
)VMt ,−VMt
].
32When the Synereo team has to hold multiple meetings and incur effort cost to explain to users when theteam burned 33% of its cryptocurrency reserves. https://synereo.com/burn-amps/
30
Figure 2: Token Price Dynamics, Stablecoin, and User Adoption.
Here the token value has two anchors. First, users need tokens for transactions. Second,
when token price declines significantly below the marginal cost of having one more unit of
token circulating, i.e., Pt ≤ −VMt/ (1 + χ), the owner optimally chooses to exchange real
resources (i.e., dollars) for tokens to reduce the supply.
Panel C of Figure 2 shows the expected token price change against mt. When mt is low,
the expectation is negative, reflecting the likely token supply increase due to payout and
labor demand (Panel A of Figure 1). The expected token price change gradually increases
and eventually becomes positive because the expected token supply change is increasingly
dominated by the declining investment (Panel A of Figure 1) and the possibility of token
buyback by the platform owners.
In Proposition 2, unlike other variables in the model that only depends on mt, the user
base Nt depends on both mt (through µPt ) and At. Panel D of Figure 2 plots the user base
dynamics with different values of At to show that as the the risk-adjusted token appreciation,
µPt , increases, the user base also increases.
31
Discussion: stablecoins. Practitioners have proposed several candidate designs for sta-
blecoin, a powerful alternative to fiat money or even digital payments through the commercial
banking system (e.g., Duffie, 2019). A popular approach is to mimic open market operation
done by central banks. When token price is low, the platform issues token bonds to buy
back tokens. Token bonds promise to pay the principal with interest in the future, but all
payments are in tokens. The problem with this design is that an inter-temporal substitution
between current and future tokens tilts the schedule of token supply over time, but it does
not introduce any real resource to support token price, nor does it provide any incentive to
economic agents to devote such resources. A champion of this design, the Basis stablecoin
project that attracted $133 million of venture capital in April 2017, has closed down all
operations, citing US securities regulation as the reason for its decision.33
An alternative design is collateralization, backing token value with real resources such
as dollar (e.g., Tether, Circle, Gemini, JPM coin, and Paxos), oil reserves (e.g., Venezuelas
El Petro, OilCoin, and PetroDollars). A derivative of such design is to further tranche the
claims on real resources, so tokens as means of payment are the most senior tranche, which
is less information-sensitive and thus has a stable secondary-market value. Such designs are
often subject to frauds and market manipulations (e.g., Griffin and Shams, 2018).
The way the buyback policy stabilizes token value differs from the existing proposals.
First, we introduce the value of platform ownership — the continuation or franchise value —
that derives value from token dividends that are optimally chosen instead of a prescheduled
bond coupons do. Then, given the economic cost of buying back tokens, χ, we characterize
the incentive for the platform owners to voluntarily buy back tokens using the numeraire
goods (real resources). The parameter χ may change, and can even be a function of macroe-
conomic state variables to better represent the cost of token buyback.
Note that it is in the interest of platform owners such as the founders to buy back
tokens, which provides an incentive-compatible support for token price. Later we introduce
commitment using smart contracting which can further help creating stablecoins.
6 Blockchain as a Commitment Device
The rise of tokens as means of payment on digital platforms is a recent phenomenon with
many applications inspired by the success of Bitcoin, Ethereum, and other blockchain-based
33https://icoexaminer.com/ico-news/133-million-basis-stablecoin-project-ceases-and-desists-citing-regulatory-concerns/
32
startups. So far, our analysis has been focusing on the case of discretionary token supply
policy of the platform – depending on the state of the world, the platform can freely adjust the
token issuance to finance platform development or to pay (or be bought back by) the owners.
The blockchain technology allows consensus protocols and token supply rules to be immune
to adjustments after the launching of platform. Next, we study platforms’ commitments to
predetermined rules of token supply. Our analysis helps understand why tokens become a
viable payment solution after the blockchain technology becomes available and what are the
welfare gains for platform owners and users from blockchain-enabled commitment.34
Specifically, we consider F (Lt, At) /Ptdt = µMMtdt, which implies a constant growth
of token supply in the interior region (dDt = 0) to finance the enhancement of platform
productivity:
dMt = F (Lt, At) /Ptdt = µMMtdt, (37)
which is popular among the blockchain applications (e.g., Ethereum) as a way to create
scarcity and avoid inflation of tokens. This rule of token supply implies that the resources
a platform gathers, Lt, is fixed given the current productivity At, token price Pt, and token
supply Mt. In our numerical solution, we use µM = 10, which is the average level of token
growth in the baseline model.
We still allow the platform owners to receive token dividends and buy back tokens, but
with Lt fixed, the owners’ only control variable is dDt and the HJB equation directly specifies
a differential equation for the value function:
rV (Mt, At) dt = maxdDt
PtdDt
[I{dDt≥0} + (1 + χ) I{dDt<0}
]+ VMt
[µMMtdt+ dDt
](38)
+ VAtAtLtµHdt+
1
2VAtAtA
2tL
2t (σ
H)2dt.
Comparing it with Equation (9), the token paid for Lt is replaced by µMMtdt. Under the
parametric choices in Section 5.1 and in the interior where dDt = 0, we have
rv (mt) = v′ (mt)mtµM + [v (mt)− v′ (mt)mt]Ltµ
H +1
2v′′ (mt)m
2tL
2t (σ
H)2, (39)
34We cannot over-emphasize the possibility of commitment brought forth by blockchains because commit-ment lies at the heart of many economic issues. For example, firms’ inability to commit to future fundingchoices has profound consequences for understanding capital structure dynamics, as Admati, DeMarzo,Hellwig, and Pfleiderer (2018) demonstrates. In fact, in the AFA presidential address in 2019, DeMarzohighlights that commitment issues are first-order in understanding capital structure dynamics and collater-alization presents one form of commitment (Demarzo, 2019).
33
Figure 3: Constant Growth of Token Supply for Platform Development.
where Lt is given by
Lt +θ
2L2t = µMPtmt. (40)
The boundary conditions are the same as those of the baseline model. Because the left-
hand side increases when Lt > −1/θ and Lt ≥ 0, so platform investment increases in Pt
and mt. Intuitively, when token is more valuable, the platform gathers more decentralized
contributions; when the token supply is high, the amount of newly issued tokens is also high
per unit of time, leading to a larger payment for Lt.
Proposition 5 (Predetermined Token Growth). Under the commitment to constant
growth of token supply for productivity enhancement, platform investment given by Equation
(40) increases in Ptmt. The owner receives token dividends (dD∗t > 0) only if Pt ≥ −VMt,
and buys back and burns tokens out of circulation (dD∗t < 0) only if −VMt ≥ Pt (1 + χ).
Token price is determined by Equation (19) as in the baseline model.
Figure 3 plots the key variables from the solution under the commitment of token growth.
Comparing Panel A of Figure 3 with Panel A of Figure 1, we can see that commitment
34
significantly increases the platform owners’ value. By comparing Panel B in the two figures,
we see that such an increase mainly comes from an about five times larger level of investment.
Therefore, a key impact commitment brings is the mitigation of under-investment.
Commitment adds value because the financing costs χ creates a conflict of interest be-
tween the platform owner and users, which manifests itself when we examine the usage value
and the investment value of tokens. To the owner, the value of tokens is −VMt , while to
the users, it is Pt. The wedge between −VMt and Pt widens as the productivity-adjusted
token supply, mt, increases and reaches χ at the buyback boundary. Therefore, as shown
in Equation (10), the financing cost translates into a dynamic cost of token issuance to
contributors that discourages investment. Intuitively, under-investment occurs because the
platform owner fully bears this dynamic token issuance cost, −VMt/Pt > 1, yet the resulting
productivity enhancement benefits both the owners (by decreasing mt and thus increasing
v (mt)) and the users (via the token usage value — a larger flow of convenience yield). More-
over, at the buyback boundary, the platform owner bears χ while the token buyback benefits
both the owner (also by decreasing mt and increasing v (mt)) and the users (through the
token investment value — the resulting token appreciation).
Commitment mitigates the under-investment problem. With commitment, the constant
growth of token supply in the interior region quarantines investment from the influence of
financing cost. As a result, investment depends directly on the state variable mt as shown
in Equation (40). When mt increases, the declining token price (Panel C of Figure 3) drives
down Lt but the increasing token supply drives up Lt. In Panel B of Figure 3, the latter
force dominates, so the large mt is, the higher platform investment, exhibiting a pattern of
investment opposite to that in the baseline model (Panel B of Figure 1).
Commitment also creates more frequent token buyback. The range of mt in Figure 3 is
reduced by one hundred times in comparison with that in Figure 1 and 2. In other words,
the platform owner is more willing to buy back and burn tokens at a much lower threshold
level of productivity-adjusted token supply. As mt increases, the ratio of owner’s token
value, −VMt , to users’ token value, Pt, increases and reaches 1 +χ at the buyback boundary.
A tighter range of mt suggests that the ratio rises faster in mt under commitment. When
investment increases in mt, an increasing amount of tokens are issued at the expense of
platform owner to boost productivity that benefits users. Therefore, as mt increases, the
divergence of owner’s and users’ interest, −VMt/Pt, becomes increasingly large, reaching 1+χ
fast and justifying token buyback at a low level of mt.
Even though the platform owner ends up paying more frequently the financing cost χ
35
under commitment, the owner’s value is still higher than the baseline model of full discretion
because the higher level of platform investment translates into a higher token value through
users expectation of productivity growth. The value added from commitment is analogous
to that in other settings of corporate finance. For example, firms’ ability to commit to future
capital-structure choices improves the firm value (Demarzo, 2019).
Stablecoins under commitment. Many blockchain applications aim for creating tokens
with stable value so that tokens may perform the roles of both means of payment and unit
of account. From a theoretical perspective, there are various merits to a unit of account
whose value is stable (e.g., Doepke and Schneider, 2017). A rigid token supply rule is
often considered as a contributing factor to price volatility because volatile demands directly
translate into price fluctuations. However, as shown in Panel D of 3, the annual volatility
of token return, dPt/Pt, is less than one basis point in spite of the 200% annual volatility of
productivity shock. The commitment to constant token growth thus brings further stability
on top of the volatility reduction that we see in the baseline model (Figure 2).35
The intuition is straightforward. Because commitment increases the sensitivity of−VMt/Pt
to mt, buyback happens at a low threshold level of productivity-adjusted token supply. As
shown in the baseline model, token buyback reduces the token volatility. When the owner
buys back tokens more frequently under commitment, volatility is reduced accordingly.
The commitment to constant token growth brought by blockchain technology not only
achieves stability of token price but also simplifies the protocol design. Moreover, since
the platform investment increases in the token market capitalization (Equation (40)), the
expected growth of platform productivity is relatively easy to calculate. In other words,
under commitment, there exists an one-to-one mapping between token market capitalization
and the enhancement of platform productivity, suggesting a simple way to rank token-based
platforms by their quality.
More broadly, our findings highlight how blockchains can potentially provide an alter-
native commitment device and in a corporate finance context, facilitates rethinking many
key issues such as capital structure. For one, it helps if a firm can commit to future financ-
ing choices or if a regulator can commit to capital requirements and leverage limits. That
35If the end goal is price stability, one can even trivially achieve perfect stability by committing to haveMt = At always, because then the driver for price dynamics, mt, becomes a constant. Here our analysis ismotivated by the tokens with constant growth rate of supply, for example, Ether.
36
said, what blockchains and smart contracts allow us to commit to is not unrestricted. We
have analyzed a plausible form of commitment here but the commitment power from the
technology in general remains a rich area for future research.
7 Conclusion
We develop a dynamic model of platform economy, where tokens are issued and used
as means of payment among users, contributors, and founding entrepreneurs. Users de-
mand tokens for their platform transactions. Dispersed contributors such as distributed
record-keepers, open-source developers, and crowdfunders make on-demand contributions to
improve the platform in exchange for token compensation. Entrepreneurs maximize their
overall seigniorage by managing token-supply dynamics, subject to the conditions that users
break even inter-temporally and labor markets are competitive.
We characterize the dynamic token allocation strategy and its implications on user base
dynamics, endogenous platform growth, the dynamics of token price. A key mechanism is
the divergence between insiders’ (entrepreneurs’) token valuation and that of outsiders (users
and workers) – when the valuation wedge falls to zero, the platform owners optimally issuing
token dividends to themselves; when it rises to an endogenously determined threshold, they
optimally burn tokens out of circulation to stabilize token value. By serving as a commitment
device, blockchains enable rule-based token supply schedule. This distinguishing feature
can help mitigate under-investment and boost platform franchise value, user adoption, and
token price. It also improves upon the novel dynamic token-supply mechanism for creating
stablecoins.
37
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40
Appendix A - A Model of Platform Transaction Surplus
In this section, we provide a theoretical foundation for our specification of transaction
surplus on the platform. Time, t ∈ R+, is continuous. The quality of the blockchain
platform, At, evolves stochastically according to a general diffusion process determined in
the equilibrium
dAt = µ(At)dt+ σ(At)dZt.
The economy is populated with a unit measure of infinitely lived risk-neutral agents who
has a discount rate r > 0. Agents have investment opportunities that occur at Poisson arrival
times, {Tn}+∞n=1, with time-varying and agent-specific intensity, λi,t. At a given Poisson time,
Tn, agent i is endowed with a technology, ωiF (·), that transforms labor into goods, and
is matched with another agent who can supply the required labor input. Agent-specific
productivity is captured by ωi. To simplify the exposition, we assume that the labor supply
has a constant marginal cost of one, and the supplier breaks even, so the full trade surplus
accrues to agent i.
Agent i’s labor demand, denoted by h, is not restricted by the real balance of token hold-
ings, Ptki,Tn−, where ki,Tn− denotes the units of tokens carried to Tn. Since the focus of this
paper is not on financial constraints, we allow the agent to borrow dollars (an instantaneous
loan) at zero cost, so h may exceed agent i’s wealth at the moment. Once the production is
complete, the loan is repaid immediately by the goods produced.
The lumpy payment for labor incurs a transaction cost that is proportional to the total
payment value, δh (δ > 0), but using tokens as means of payment save the transaction
cost by U (Ptki,Tn−) (U ′ > 0, U ′′ < 0) because agent i does not need to exchange dollars
for tokens, the required means of payment on the platform. This transaction cost can be
interpreted as the cost of traditional bank transfer service, legal costs of contracting. Native
tokens in many cases allow transaction parties unknown and untrusted to still complete a
value transfer at distance, or to contract on simple terms, thanks to the blockchain ledger
and smarting contracting functionalities. For these reasons, platforms such as Kin require
all on-platform transactions to be mediated using Kin tokens.
Agent i maximizes the investment profit, which is a jump in wealth,
maxh
ωiF (h)− h− (δh− U (Ptki,Tn−)) , (41)
where the last term is the transaction cost. The optimal labor demand, h∗, is given by
ωiF′ (h∗) = 1 + δ, (42)
so that the marginal value of production is equal to the marginal cost of labor plus the
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transaction cost, δ. We can substitute the constant h∗ into the investment profit to have
ωiF (h∗)− (1 + δ)h∗ + U (Ptki,Tn−) . (43)
We assume that ωi is sufficiently high so h∗ ≥ Ptki,Tn−. The conversion between the local
currency (token) and other assets can be costly, especially when a lumpy transaction is
required within a short period of time. By holding tokens, agents save such costs.
Therefore, at time t, agent i has an expected gain of λi,tU (Ptki,t) dt by holdings ki,tunits of tokens for dt. To obtain a tighter analytical characterization of the equilibrium,
we specify λi,t = (Nγt Ate
ui)α (α ∈ (0, 1)). A larger community (Nt) makes it easier to find
transaction counterparties. A higher platform quality (At) makes matching more efficient.
And ui captures agent-specific transaction needs. We specify U (Ptki,t) = χ (Ptki,t)1−α, so
the expected transaction costs saved are
λi,tU (Ptki,t) = (Nγt Ate
ui)α (Ptki,t)1−α χdt. (44)
In the model we normalize χ = 1 because its scaling effect can be subsumed by the level of
At.
We may reinterpret h as goods or services other than labor, and the investment profit as
a burst of consumption or utility value from transactions. The features our micro-foundation
captures are two-fold: (i) the arrival of transaction opportunities depends on the user base,
the platform quality, and agent-specific factors; (ii) holding tokens on the tokenized platform
save transaction costs for lumpy payments. In essence, we model the flow utility of token
holdings as a form of convenience yield, as emphasized by John Cochrane.36
We have many applications of native tokens as means of payment on platforms. In the
case of Kin, entrepreneurs obtain information from consumer surveys that helps improve
product quality. Consumers are rewarded by the native currency, Kin tokens. In our model,
we do not differentiate buyers and sellers among users because in reality, the one entrepreneur
are often consumers of other sellers’ products in the platform market place. They can
simultaneously take on different roles (investor, user, developer or operator), and actively
participate in a sharing economy.
36Please refer to https://johnhcochrane.blogspot.com/2017/11/bitcoin-and-bubbles.html
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